1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NeTakaya
3 years ago
11

Consider a population list x with μx=10 and SDx = 1. A second population list, y, with μy=10 and SDy=2, is added to the first li

st. Assuming the same population size for both lists, what is the SD of the new combined list?
Mathematics
1 answer:
Basile [38]3 years ago
3 0

Answer:

The combined standard deviation is 1.58114.

Step-by-step explanation:

The formula to compute the combined standard deviations of two different data sets is:

SD_{c} =\sqrt{\frac{n_{X}S^{2}_{X}+n_{2}S^{2}_{Y}+n_{X}(\mu_{X}-\mu_{c})^{2}+n_{Y}(\mu_{Y}-\mu_{c})^{2}}{n_{X}+n_{Y}}

Here \mu_{c} is the combined mean given by:

\mu_{c}=\frac{n_{X}\mu_{X}+n_{Y}\mu_{Y}}{n_{X}+n_{Y}}

It is provided that the sample size is same for both the data sets, i.e.n_{X} = n_{Y}=n

Compute the combined mean as follows:

\mu_{c}=\frac{n_{X}\mu_{X}+n_{Y}\mu_{Y}}{n_{X}+n_{Y}}\\=\frac{(n\times10)+(n\times10)}{n+n}}\\=\frac{20n}{2n}\\ =10

Compute the combined standard deviation as follows:

SD_{c} =\sqrt{\frac{n_{X}S^{2}_{X}+n_{2}S^{2}_{Y}+n_{X}(\mu_{X}-\mu_{c})^{2}+n_{Y}(\mu_{Y}-\mu_{c})^{2}}{n_{X}+n_{Y}}}\\=\sqrt{\frac{(n\times1^{2})+(n\times2^{2})+(n(10-10))+(n(10-10))}{n+n}}\\=\sqrt{\frac{n+4n}{2n} } \\=\sqrt{\frac{5n}{2n} } \\=\sqrt{\frac{5}{2}} \\=1.58114

Thus, the combined standard deviation is 1.58114.

You might be interested in
In the image below, ABC ~ DEF What is the length of EF and the measure of D
Gwar [14]
If triangle ABC is congruent to triangle DEF, then EF = BC = 27
This is because BC and EF are the last two letters of ABC and DEF respectively. They match up and correspond, being congruent by CPCTC

-------------------------------------------------------------------------------------------------------------

Similarly, if triangle ABC is congruent to triangle DEF, then angle D = angle A = 49 degrees

The letter D and the letter A are the first letters of DEF and ABC respectively. So they match up and are congruent by CPCTC

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

-------------------------------------------------------------------------------------------------------------

So in short, the answer is choice B) 27; 49

7 0
3 years ago
Which is true about the functional relationship shown in the graph?
Snowcat [4.5K]
We need a picture of the graph
8 0
3 years ago
Find the inverse of the function f f (x )<br><br> equals 9 x + 7
MrMuchimi

<em>Note: Your question seems a little bit ambiguous. So, I am assuming the given function f(x)=9x+7.</em>

<em>Thus, I am solving based on it. It would still clear your concept. </em>

Answer:

The inverse of f(x)=9x+7

  • \frac{x-7}{9}

Step-by-step explanation:

Given the function

f(x)=9 x + 7

A function g is the inverse of function f if for y=f(x), x=g(y)

Replace x with y

x=9y+7

solve for y

9y=x-7

y=\:\frac{x-7}{9}

Therefore,

The inverse of f(x)=9x+7 is:

  • \frac{x-7}{9}

i.e.

\mathrm{Inverse\:of}\:9x+7:\quad \frac{x-7}{9}

6 0
3 years ago
Need hello fast I don’t know what to do
Free_Kalibri [48]

35 + 14
The greatest common factor for both is 7. Factor out 7

7(5 + 2) is your answer

Hope this helps

8 0
3 years ago
Find the distance between (1,2) and ( 7,2
OLga [1]
The distance between these points are 6
4 0
3 years ago
Other questions:
  • Expand and simplify (5x+2)(2x-3)
    5·2 answers
  • 10 POINTS<br> Find x. Assume that segments that appear tangent are tangent.
    10·1 answer
  • Solve. -15 = -6n – 3 + 6
    15·2 answers
  • 3(4x) = (3times4)x property
    6·1 answer
  • I don't know how to work it out. show work pls
    14·1 answer
  • I need help finding the pattern!!!!
    6·1 answer
  • A technology research group recently published a report on computer programmers’ views about a game development program. The rep
    5·2 answers
  • Simplify <br><br> y = -1x - 1<br><br> pls hurryyyyyyy
    11·1 answer
  • 1/3•9•5 Dot means multiply
    11·1 answer
  • Point O is the centroid of triangle ABC. If OD=3x -2 and OC= 5x, find x.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!